Letters to the Editor

Letters to the editor will be confined to discussions of papers that have appeared in The American Statistician and to important issues facing the statistical community. Letters discussing papers in The American Statistician must be received within two months of publication of the paper; the author of the paper will then be given an opportunity to reply, and the letters and reply will be published together. All letters to the editor will be refereed. Corrections of errors that have been noted in papers published in The American Statistician will be listed as corrections at the end of this section.     

Letters to the Editor

Letters to the editor will be confined to discussions of papers that have appeared in The American Statistician and of important issues facing the statistical community. Letters discussing papers in The American Statistician must be received within two months of publication of the paper; the author of the paper will then be given an opportunity to reply, and the letters and reply will be published together. All letters to the editor will be refereed. Corrections of errors that have been noted in papers published in The American Statistician will be listed as corrections at the end of this section.     

Discipline-Specific Literature Bases: A View of the APS Model

Abstract

Librarians see the large quantities of literature and the complete writing/publishing/world as a complete system. Changes to one piece (e.g., making publishing or reading electronic) will not fundamentally change the process. The pieces of the system are there, not for technological reasons, but for reasons of authority, validation, and self-correction in the process of scholarly communication. Electronic publishing will cause great changes, but the changes will not eliminate roles that now exist. The changes will be to enhance our abilities to better do that which we do now, whether that be to edit, review, referee, write, or manage the information flow.     

Statistics development: statistical methods meeting the user’s needs

Statistical methods have the potential of being effectively used by industrial practitioners if they satisfied two criteria: functionality and usability. Statistical methods are usually the product of statistical research activities of universities and other research organizations. Some already satisfy these criteria; however, many do not. The effect is that potentially relevant methods are not used in practice as often as they could be. In this paper we will present an approach regarding ‘statistics development,’ in which the end-user is given a central position, so that the results from statistical research aim to meet the needs and requirements of the practitioner. Examples of known and new methods will be presented, and we will discuss issues such as education in statistics, the link with statistical consultancy and publication of methods through various channels.     

A Study of Some Different Concepts of Symmetry on the Real Line

Recently, different concepts of symmetry on R ⁺ such as R-symmetry, log-symmetry, and double symmetry are studied. Analogous concepts and their properties of these symmetries on R will be studied in this work. Based on skewing representation and previous studies, characterizations of double symmetry on R will be given. Among others, some interesting examples of the so-called I-symmetry, that is the analogue of log-symmetry on R, will also be presented.     

Tests for the Validity of the Assumption that the Underlying Distribution of Life is Pareto

This article considers the problem of testing the validity of the assumption that the underlying distribution of life is Pareto. For complete and censored samples, the relationship between the Pareto and the exponential distributions could be of vital importance to test for the validity of this assumption. For grouped uncensored data the classical Pearson χ² test based on the multinomial model can be used. Attention is confined in this article to handle grouped data with withdrawals within intervals. Graphical as well as analytical procedures will be presented. Maximum likelihood estimators for the parameters of the Pareto distribution based on grouped data will be derived.     

Three Recommendations for Improving the Use of p-Values

ABSTRACT

Researchers commonly use p-values to answer the question: How strongly does the evidence favor the alternative hypothesis relative to the null hypothesis? p-Values themselves do not directly answer this question and are often misinterpreted in ways that lead to overstating the evidence against the null hypothesis. Even in the “post p?<?0.05 era,” however, it is quite possible that p-values will continue to be widely reported and used to assess the strength of evidence (if for no other reason than the widespread availability and use of statistical software that routinely produces p-values and thereby implicitly advocates for their use). If so, the potential for misinterpretation will persist. In this article, we recommend three practices that would help researchers more accurately interpret p-values. Each of the three recommended practices involves interpreting p-values in light of their corresponding “Bayes factor bound,” which is the largest odds in favor of the alternative hypothesis relative to the null hypothesis that is consistent with the observed data. The Bayes factor bound generally indicates that a given p-value provides weaker evidence against the null hypothesis than typically assumed. We therefore believe that our recommendations can guard against some of the most harmful p-value misinterpretations. In research communities that are deeply attached to reliance on “p?<?0.05,” our recommendations will serve as initial steps away from this attachment. We emphasize that our recommendations are intended merely as initial, temporary steps and that many further steps will need to be taken to reach the ultimate destination: a holistic interpretation of statistical evidence that fully conforms to the principles laid out in the ASA statement on statistical significance and p-values.     

Distribution of angles between unit vectors and the multiple comparison problem for unit vectors

We suppose that L x i = Fq(μi, KiK) for i=1,...,p, where the independent Fisher distributions on the unit sphere in Rq have modal vectors μi and known concentrations KiK, where K will be large—in fact, to obtain asymptotic distributions, we will let K tend to infinity. The term x'iXj=cos 0ij estimates cos 0ij= μiμy. The asymptotic joint distribution of the terms will be studied when all the vectors μi μ are distinct, and for the special case when all the vectors μi=μ, so that all the terms are zero. These very different results have a variety of applications as well as being interesting in themselves. One of these applications is the 'multiple comparisons problem' for unit vectors. However, it was found necessary to give here a different way of solving this problem.     

利用菲德模型测量教育投资的外溢效应

一、教育投资经济效益的理论探讨在现代社会中 ,教育的作用和影响是多方面的 ,教育既具有经济职能又具有社会职能。教育投资的经济效益是教育发挥其经济职能的表现。教育投资的经济效益 (简称教育的经济效益 ,是指通过教育再生产出一定数量和质量的人才 ,进而提高社会劳动生产率 ,促进国民经济的增长 ,在其增长总额中抵偿用于教育和培养的全部经费之后的余额。对于教育投资的经济效益的计量 ,由于教育的经济效益的复杂性及理论研究的欠缺 ,至今没有一个理想的统一标准。目前 ,具有代表性的几种计量方法主要有 :(1) )舒尔茨的余数分析法。舒…     

市场化程度、政府治理、制度安排与反腐败关系——基于2000—2013年宏观面板数据的分析

腐败治理是一项复杂的社会工程。目前,中国进入全面深化改革的新时期,如何处理好反腐败与市场经济改革、政府治理、制度安排之间的关系,成为当前改革的重点与难点。利用中国2000—2013年宏观面板数据,系统分析了市场化程度、政府治理和制度安排因素对反腐败的影响机制。研究发现:市场化程度提升能够起到消减腐败的作用。政府治理对反腐败影响较为复杂,政府规模表现为规模越大,治理能力越完善,越有助于减少腐败,但子指标公职人员相对工资水平与反腐败相关性较为模糊,需要理性看待现阶段"高薪养廉"的作用。制度安排特别是法治化和信息化水平的提升起到了显著减少腐败的作用,佐证了全面推进依法治国和加强信息化建设对反腐倡廉的必要性。     

农产品电商不同融资方式选择的影响因素研究

基于2 131份有效调查问卷数据,运用有序Probit模型对农产品电商不同融资方式选择的影响因素进行研究。研究发现:农产品电商选择从P2P等非正规金融机构融资,还是从农村信用社等正规金融机构融资,这与农产品电商的户主禀赋变量、家庭特征变量及区域特征变量紧密相关;在户主禀赋变量、家庭特征变量和区域特征变量方面具有优势的农产品电商,更倾向于从P2P等非正规金融机构融资,反之,则倾向于从农村信用社等正规金融机构融资。     

Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with mixture models. Furthermore, in some of the examples we could exploit INLA within MCMC to make joint inference on an ensemble of model parameters.     

Suitable Algorithm Associated with a Parameterization for the Three-Parameter Log-Normal Distribution

Associated with a parameterization for the three-parameter lognormal distribution, an algorithm was proposed by Komori and Hirose, which can find a local maximum likelihood (ML) estimate surely if it exists. Nevertheless, by Vera and Díaz-García it was shown that performance in finding a local ML estimate deteriorated by adopting the parameterization only and using other algorithm. In the present article, it will be shown that Komori and Hirose’s algorithm should be used for the parameterization. This work will also give MATLAB codes as a useful tool for the parameter estimation of the distribution.     

Description of a subfamily of the discrete pearson system as generalized-binomial distributions

In this paper we prove that a subfamily of distributions of the discrete Pearson, system, containing the Pólya distribution without replacement and hence the hypergeometric distribution, can be described as generalized-binomial distributions, i.e., the distribution of the number of successes which occur in independent trials. It is also shown that the probability of success will necessarily be different in each trial, with the exception of deterministic ones. As a consequence, all the properties of the generalized-binomial distribution will apply to this subfamily. Thus, applications to hypothesis testing and confidence intervals in the Pólya distribution are considered.     

Scenarios, Uncertainty and Conditional Forecasts of the World Population

Current official population forecasts differ little from those that Whelpton made 50 years ago either in the cohort–component methodology used or in the arguments used to motivate the assumptions. However, Whelpton produced some of the most erroneous forecasts of this century. This suggests that current forecasters should ensure that they give users an assessment of the uncertainty of their forecasts. We show how simple statistical methods can be combined with expert judgment to arrive at an overall predictive distribution for the future population. We apply the methods to a world population forecast that was made in 1994. Accepting that point forecast, we find that the probability is only about 2% that the world population in the year 2030 will be less than the low scenario of 8317 million. The probability that the world population will exceed the high scenario of 10 736 million is about 13%. Similarly, the probability is only about 51% that the high–low interval of a recent United Nations (UN) forecast will contain the true population in the year 2025. Even if we consider the UN high–low intervals as conditional on the possible future policies of its member states, they appear to have a relatively small probability of encompassing the future population.     

A Note on Comparing the Power of Test Statistics at Low Significance Levels

It is an obvious fact that the power of a test statistic is dependent upon the significance (alpha) level at which the test is performed. It is perhaps a less obvious fact that the relative performance of two statistics in terms of power is also a function of the alpha level. Through numerous personal discussions, we have noted that even some competent statisticians have the mistaken intuition that relative power comparisons at traditional levels such as α=0.05 will be roughly similar to relative power comparisons at very low levels, such as the level α=510^?8, which is commonly used in genome-wide association studies. In this brief note, we demonstrate that this notion is in fact quite wrong, especially with respect to comparing tests with differing degrees of freedom. In fact, at very low alpha levels the cost of additional degrees of freedom is often comparatively low. Thus we recommend that statisticians exercise caution when interpreting the results of power comparison studies which use alpha levels that will not be used in practice.     

Order Statistics from the Generalized Exponential Distribution and Applications

With linear dispersion effects, the standard factorial designs are not optimal estimation of a mean model. A sequential two-stage experimental design procedure has been proposed that first estimates the variance structure, and then uses the variance estimates and the variance optimality criterion to develop a second stage design that efficiency estimates the mean model. This procedure has been compared to an equal replicate design analyzed by ordinary least squares, and found to be a superior procedure in many situations.

However with small first stage sample sizes the variance estiamtes are not reliable, and hence an alternative procedure could be more beneficial. For this reason a Bayesian modification to the two-stage procedure is proposed which will combine the first stage variance estiamtes with some prior variance information that will produce a more efficient procedure. This Bayesian procedure will be compared to the non-Bayesian twostage procedure and to the two one-stage alternative procedures listed above. Finally, a recommendation will be made as to which procedure is preferred in certain situations.     

Longitudinal dynamic analyses of cognition in the health and retirement study panel

The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.     

Separation and Lack of Separation of Subpopulation in the Mixed Distributions

This is a comparative study between the estimates of parameters of mixed distributions in the case of the possibility of separating the units of subpopulation or the absence of that possibility under the progressive type I censored test data. An iterative procedure is developed and tested numerically to obtain new estimators and their variance–covariance matrix. Finally, we will use the exact distribution of the maximum likelihood estimators as well as its asymptotic distribution and the parametric bootstrap method; then, we will discuss the construction of confidence intervals for the mean parameter and their performance is assessed through Monte Carlo simulations.